Help with Modeling Shotgun Handle
I'm lazy, so I'd let Blender do most of the job.
Make the rectangular part and the round part, and let Blender make the transition for you.

A nice final render (to boost my ego)


Project blend file for your inspiration:


01) Square part
- Start with a basic cube, add loopcuts, extrude it and stuff...
- Use proportional editing (I used Sharp profile)
- Use subsurf modifier  

Use proportional editing for those tapered edges


02) Round part
- I used a basic cylinder and extruded it.
- Just make sure the number of vertices (and edges) is the same as in the open loop of the square part.
It's 24 vertices (and edges) in this case.  

03) Bridge Edge loops
- Select and bridge the two edge loops (Edge > Bridge Edge Loops)
- Both loops need to have the same number of vertices
- Both meshes need to be in one object (you can join them into one with Ctrl+J)